Problem 4. Let X = (X₁, X2,..., Xn) be i.i.d. where each X, has proba- bility mass function P(X = ) - (9) (1-0)¹-1, ₁ € (-1,0,1}, 0≤ 0≤1.
Problem 4. Let X = (X₁, X2,..., Xn) be i.i.d. where each X, has proba- bility mass function P(X = ) - (9) (1-0)¹-1, ₁ € (-1,0,1}, 0≤ 0≤1.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Problem 4. Let X = (X₁, X2,..., Xn) be i.i.d. where each X, has proba-
bility mass function
P(Xi = x₁) =
0
(1-0)¹-il, a; € (-1,0,1), 0≤0≤1.
a. Derive the MLE Ô for 0.
b. Assuming n is large, find the approximate distribution of .
c. Find an approximate 95% confidence interval for 0.
d. Derive the likelihood ratio test for testing 0 = 1/2 vs. 0 > 1/2.
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